Patent Document 1 describes compounds (I) and (II), which are useful as anti-HIV drugs and shown by formulae:
This document describes the following reaction formula as a method of producing compound (I).

Furthermore, Patent Documents 2 to 6 describe the following reaction formula as an improved method of producing compound (I).

However, the above production methods of these documents are not satisfactory for the industrial manufacturing method because of the followings:
these reaction processes for obtaining compound (I) include 16 or 11 steps, respectively, and are very long,
the total yield is low, thus being inefficient,
a high toxic and harmful reaction is used.
an expensive reagent is used,
an environmentally harmful reagent is used.
Therefore, the development of a method for more efficient industrial mass-production of compound (I), compound (II) and their derivatives has been desired.
Non-Patent Documents 1 and 2 describe a method of producing pyrane-4-one and pyridine 4-one. Patent Document 7 and Non-Patent Document 3 describe a method of producing enaminone derivatives. However, a method of producing pyronediester and pyridonediester of the present invention is not described in these documents. Furthermore, a method of manufacturing compounds having HIV-integrase inhibitory activity by using the production method of the present invention is not disclosed. Patent Document 8 is an international patent application by the present applicant. Though this document describes the method of producing pyronediester and pyridonediester identical to the present invention, compounds having HIV-integrase inhibitory activity and anti-HIV drugs are not described therein.